Question

For a group of 50 male workers, the mean and standard deviation of their hourly wages are 263
and 9 respectively. For a group of 40 female workers, there are 54 and respectively. The
standard deviation of hourly wages for the combined group of workers is?
a) 7
b) 8
c) 6
d) 9​

Answer 1

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Answer 2

The question lacks some information, however the correct one is - For a group of 50 male worker, the mean and standard deviation of their weekly wages are Rs 63 and Rs 9 respectively and for a group of 40 female workers, the measures are respectively Rs 54 and Rs 6 . Find the standard deviation for combined group workers.

Combined standard deviation for group of workers = 9 (Given)

Weekly wages mean of male workers  x1 =63

Weekly wages mean of female workers  x2 =54

Standard deviation of weekly wages of the male workers σ1 =9

Standard deviation of weekly wages of the female workers σ2 =6

Thus,The combined mean will be -

= x =n1 x1+n2 x2n1+n2                

= 50 × 63 + 40 × 54/50+40                                    

=3150 +2160/90                                      

=5310/90        

= 59

Now,

d1 =  ∣x− x1∣= 59−63 = 4

d2= ∣x− x2∣ =59−54 = 5

The combined standard deviation σ is -

= √n1 ( σ1²+d1²) +n2( σ2²+d2²)/n1+n2                                

= √50 × (9²+4²) + 40 × (6²+5²) /50+40

= √50 × (81+16) +40 × (36+25) /90                        

= √4850+2440/90                          

= √81

= 9